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Contribution of Two-Boson-Exchange with $Δ(1232)$ Excitation to Parity-Violating Elastic Electron-Proton Scattering

We study the leading electroweak corrections in the precision measurement of the strange form factors. Specifically, we calculate the two-boson-exchange (TBE), two-photon-exchange (TPE) plus $γZ$-exchange ($γZ$E), corrections with $Δ(1232)$ excitation to the parity-violating asymmetry of the elastic electron-proton scattering. The interplay between nucleon and $Δ$ contributions is found to depend strongly on the kinematics, as $δ_Δ$ begins as negligible at backward angles but becomes very large and negative and dominant at forward angles, while $δ_N$ always stays positive and decreases monotonically with increasing $ε$. The total TBE corrections to the extracted values of $G^{s}_{E}+βG^{s}_{M}$ in recent experiments of HAPPEX and G0 are, depending on kinematics, found to be large and range between 13% to -75% but small in the case of A4 experiments.